Optimization Study of the Shear Moduli of Magnetic Foil-Sheet and Its Implication into the Noise Simulation

The investigation builds upon a modal testing campaign conducted on a specimen composed of 40 bonded laminations of domain-refined GO electrical steel, and extends analytical approach described by Agarwal et al. [1]. The sample was excited using an electrodynamic shaker, and its vibrational response was captured via laser vibrometry. The experimental resonance frequencies were then used to calibrate a Finite Element (FE) model where the material was treated as orthotropic. The optimization process, aimed to minimize the deviation between experimental and numerical resonance frequencies by tuning key mechanical parameters:

Young’s moduli (rolling and cross-rolling directions), Poisson’s ratios, and the shear modulus.

The results yielded a shear modulus of approximately 132.6 GPa, with a Poisson’s ratio of 0.484

(cross-roll to roll). These values enabled the FE model to replicate the experimental resonance frequencies with deviations below 2.5%, validating the robustness of the optimization approach. Furthermore, the identified parameters were cross-validated using an analytical orthotropic model, showing strong agreement with reference data from the CRGO manufacturer and data available in publications [2].

The implications of this study are twofold. First, it provides a reliable methodology for characterizing the shear modulus of GO steels, which can be extended to other magnetic materials. Second, it enhances the fidelity of noise simulations in transformer design by enabling more accurate assignment of mechanical properties in FE vibroacoustic models. This is particularly relevant for predicting the impact of Maxwell forces and magnetostrictioninduced vibrations on acoustic emissions.

Despite the study’s reliance on a single specimen and manual assembly, the results are considered representative due to the negligible influence of adhesive thickness and lamination misalignment. The methodology is scalable and adaptable for broader material characterization efforts in electrical steel applications.